I haven't shaved my armpits in almost 3 years and do not notice more stinky BO. What does affect my BO is what I eat or drink, or you know if I haven't showered for a couple days(there's no water here in California). My BO was MUCH worse when I shaved and drank coffee or tea.
I decided to shave my legs for summer because my hair is darker than most men's leg hair and just as long if not longer.